Neco Model Questions Vol1 2019 Agricultural Science Question 40

An extension officer aims to introduce a new drought‑resistant sorghum variety to 120 farmers. Adoption follows the logistic model \(A(t)=\frac{K}{1+e^{-b(t-t_0)}}\) where \(K=120\), the adoption coefficient \(b\) is 0.4 month\(^{-1}\) without any demonstration farms, and \(t_0\) is the month when half the farmers have adopted. Initially, after 4 months, 30 farmers have adopted the variety. Each demonstration farm increases \(b\) by 0.1 month\(^{-1}\) and costs ₦50 000. The officer has a budget of ₦200 000 and wants at least 90 % of the farmers (i.e., 108 farmers) to adopt within 12 months. Determine the minimum number of demonstration farms required and state whether the budget is sufficient. Present your answer as "Number of farms: X; Budget sufficient: Yes/No".